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A hierarchical structure of observer-based adaptive fuzzy-neural controller for MIMO systems. (English) Zbl 1238.93054

Summary: An observer-based adaptive controller developed from a hierarchical fuzzy-neural network (HFNN) is employed to solve the controller time-delay problem for a class of multi-input multi-output (MIMO) non-affine nonlinear systems under the constraint that only system outputs are available for measurement. By using the implicit function theorem and Taylor series expansion, the observer-based control law and the weight update law of the HFNN adaptive controller are derived. According to the design of the HFNN hierarchical fuzzy-neural network, the observer-based adaptive controller can alleviate the online computation burden. Moreover, the common adaptive controller is utilized to control all the MIMO subsystems. Hence, the number of adjusted parameters of the HFNN can be further reduced. In this paper, we prove that the proposed observer-based adaptive controller can guarantee that all signals involved are bounded and that the outputs of the closed-loop system track asymptotically the desired output trajectories.

MSC:

93C40 Adaptive control/observation systems
93A13 Hierarchical systems
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[1] Tong, S.; Li, H. X., Direct adaptive fuzzy output tracking control of nonlinear systems, Fuzzy Sets Syst., 126, 107-115 (2002) · Zbl 0995.93512
[2] Narendra, K. S.; Annaswamy, A. M., Stable Adaptive Systems (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0758.93039
[3] Sastry, S. S.; Bodson, M., Adaptive Control: Stability, Convergence, and Robustness (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0721.93046
[4] Wang, M.; Chen, B.; Dai, S. L., Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems, Fuzzy Sets Syst., 158, 2655-2670 (2007) · Zbl 1133.93350
[5] Zekri, M.; Sadri, S.; Sheikholeslam, F., Adaptive fuzzy wavelet network control design for nonlinear systems, Fuzzy Sets Syst., 159, 2668-2695 (2008) · Zbl 1170.93351
[6] Ioannou, P. A.; Sun, J., Robust Adaptive Control (1996), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0839.93002
[7] Liu, Z.; Li, H. X., A probabilistic fuzzy logic system for modeling and control, IEEE Trans. Fuzzy Syst., 13, 848-859 (2005)
[8] Slontine, J. J.E.; Li, W., Applied Nonlinear Control (1991), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[9] Liu, Z.; Li, C., Fuzzy neural network quadratic stabilization output feedback control for biped robots via \(H^\infty\) approach, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 33, 67-84 (2003)
[10] Krsti, M.; Kokotovi, P. V., Control Lyapunov functions for adaptive nonlinear stabilization, Syst. Control Lett., 26, 17-23 (1995)
[11] Wang, L. X., Stable adaptive fuzzy control of nonlinear systems, IEEE Trans. Fuzzy Syst., 1, 146-155 (1993)
[12] Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V., Nonlinear and Adaptive Control Design (1995), Wiley: Wiley New York · Zbl 0763.93043
[13] Marino, R.; Tomei, P., Nonlinear Control Design: Geometric, Adaptive, & Robust (1995), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0833.93003
[14] Nijmeijer, H.; van der Schaft, A. J., Nonlinear Dynamical Control Systems (1990), Springer-Verlag: Springer-Verlag New York · Zbl 0701.93001
[15] J.D. Bošković, L. Chen, R.K. Mehra, Multivariable adaptive controller design for a class of non-affine models arising in flight control, in: Conference on Decision Control, Orlando, 2001, pp. 2442-2447.; J.D. Bošković, L. Chen, R.K. Mehra, Multivariable adaptive controller design for a class of non-affine models arising in flight control, in: Conference on Decision Control, Orlando, 2001, pp. 2442-2447.
[16] Lane, S. H.; Stengel, R. F., Flight control design using nonlinear inverse dynamics, Automatica, 24, 471-483 (1988) · Zbl 0649.93051
[17] Bošković, J. D.; Chen, L.; Mehra, R. K., Adaptive control design for nonaffine models arising in flight control, AIAA J. Guid. Control Dyn., 27, 209-217 (2004)
[18] Byrnes, C. I.; Ho, X., The zero dynamics algorithm for general nonlinear system and its application in exact output tracking, J. Math. Syst. Estimation Control, 3, 51-72 (1993) · Zbl 0770.93048
[19] D. Nešić, E. Skafidas, I.M.Y. Mareels, R.J. Evans, Analysis of minimum phase properties for non-affine nonlinear systems, in: Conference on Decision Control, San Diego, CA, 1997, pp. 606-611.; D. Nešić, E. Skafidas, I.M.Y. Mareels, R.J. Evans, Analysis of minimum phase properties for non-affine nonlinear systems, in: Conference on Decision Control, San Diego, CA, 1997, pp. 606-611.
[20] Nešić, D.; Skafidas, E.; Mareels, I. M.Y.; Evans, R. J., Minimum phase properties for input nonaffine nonlinear systems, IEEE Trans. Autom. Control, 44, 868-872 (1999) · Zbl 1073.93536
[21] Leu, Y. G.; Wang, W. Y.; Lee, T. T., Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems, IEEE Trans. Neural Networks, 16, 853-861 (2005)
[22] Leu, Y. G.; Wang, W. Y.; Lee, T. T., Robust adaptive fuzzy-neural controller for uncertain nonlinear systems, IEEE Trans. Robotics Automat., 15, 805-817 (1999)
[23] Leu, Y. G.; Lee, T. T.; Wang, W. Y., Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 29, 583-591 (1999)
[24] Chen, B.; Tong, S.; Liu, X., Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes, Fuzzy Sets Syst., 158, 1097-1125 (2007) · Zbl 1113.93068
[25] Chen, B.; Liu, X., Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach, IEEE Trans. Fuzzy Syst., 13, 832-847 (2005)
[26] Liu, Y. J.; Wang, W., Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems, Inf. Sci., 177, 3901-3917 (2007) · Zbl 1121.93037
[27] Yang, Y.; Zhou, C., Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach, Inf. Sci., 170, 211-234 (2005) · Zbl 1068.93037
[28] Liu, Y. J.; Wang, W.; Tong, S. C.; Liu, Y. S., Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 40, 170-184 (2010)
[29] Liu, Y. J.; Tong, S. C.; Wang, W., Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems, Fuzzy Sets Syst., 160, 2727-2754 (2009) · Zbl 1176.93046
[30] Wang, W. Y.; Chien, Y. H.; Leu, Y. G.; Lee, T. T., Adaptive T_S fuzzy-neural modeling and control for general MIMO unknown nonaffine nonlinear systems using projection update laws, Automatica, 46, 852-863 (2010) · Zbl 1191.93073
[31] Liu, Y. J.; Tong, S. C.; Li, T. S., Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems, Fuzzy Sets Syst., 164, 25-44 (2011) · Zbl 1217.93090
[32] Hwang, M. C.; Hu, X., A robust position/force learning controller of manipulators via nonlinear H-infinity control and neural networks, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 30, 310-321 (2000)
[33] Leu, Y.-G.; Wang, W.-Y., Output feedback adaptive fuzzy control for manipulators, Dyn. Continuous Discrete Impulsive Syst. Ser. B Appl. Algorithms, 3, 1194-1198 (2007)
[34] Zeng, X. J.; Keane, J. A., Approximation capabilities of hierarchical hybrid systems, IEEE Trans. Syst. Man Cybern. Part A, 36, 1029-1039 (2006)
[35] Li, I. H.; Wang, W. Y.; Su, S. F.; Lee, Y. S., A merged fuzzy neural network and its applications in battery state-of-charge estimation, IEEE Trans. Energy Convers., 22, 697-708 (2007)
[36] Zeng, X. J.; Keane, J. A., Separable approximation property of hierarchical fuzzy systems, IEEE Conf. Fuzzy Syst., 951-956 (2005)
[37] Khalil, H. K., Nonlinear Systems (1992), Macmillan: Macmillan New York · Zbl 0626.34052
[38] Leu, Y. G.; Lee, T. T.; Wang, W. Y., Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems, IEEE Trans. Syst. Man Cybern. B Cybern., 29, 583-591 (1999)
[39] Lee, C. H.; Chien, J. C.; Chang, H. H.; Kuo, C. T.; Chang, H. H., Direct adaptive backstepping control for a class of MIMO non-affine systems using recurrent neural networks, (International MultiConference of Engineers and Computer Scientists, vol. 1 (2009))
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